April, 1911. 



KNOWLEDGE. 



133 



it is necessary to investigate tlie personal errors ; 

 one that depends upon the magnitude of the various 

 stars, and the other which de[)ends upon the direction 

 of movement of the stars in the lield of view in the 

 telescope. These errors are to be studied for e\'ery 

 one of the observers of the commission. 



FUNDAMKNTAL METHOD. 



Of great importance is the use of the fundamental 

 method, in the determination of the meridian line 

 and for the correction of the astronomical clock. 

 In the usual method the principal stars have served 

 for these objects. One used one of the equatorial 

 stars for determining the correction of the clock, 

 and two of the circumpolar stars served for fixing the 

 azimuth of the instrument or direction of the 

 meridian. But in this simple use of the positions of 

 the stars the errors of the positions adopted come 

 into the calculations. 



In the fundamental method, however, one does not 

 adopt the positions of the stars, though they are better 

 determined. In all there are some systematic errors : 

 the errors of the obser\-ations. and the proper motions 

 of the stars, during the years since they w ere revised. 

 come in. 



Each time that there is a new revision it is 

 probable that the data is more exact. The object of 

 the revision is to adjust all parts of the area of 

 positions in such a way that no differences have 

 entered into the results of the observations when 

 thev are made in the various regions of the sky, 

 though it is necessary to use the positions of the 

 stars in opposite parts. In the measurement of 

 small arcs there are no great difficulties, tlie errors 

 are unimportant : but in the fundamental method 

 it is necessar\- to measure great arcs, even a complete 

 circumference. In general the errors w ill be greater, 

 and onl\- by much attention to the observations and 

 calculations can we avoid the increase of these 

 indeterminable differences. 



This is the first time that the fundamental method 

 has been employed, to its fullest extent, in a South 

 American observatory. In the fundamental method 

 the direction of the meridian will be fixed by the 

 transits of the same stars made above and below the 

 pole. In this case the error of position adopted will 

 have no increasing influence in the computations. 



Instrumental Corrections. 



The latitude will be determined b\- the same 

 circumpolar stars. Other stars which come above 

 and below the pole will serve for a fundamental 

 determination of refraction. For this purpose the 

 stars more distant from the pole, which transit at a 

 small altitude, are selected. It is necessary to study 

 the refraction at each place, especially when the 

 observatory is at a considerable altitude above the 

 level of the sea. For this study we have the com- 

 bination of the observations at Albany with those at 

 San Luiz. At one place it will be possible to 

 observe the stars which pass in the zenith of the 

 other, and verify, or ascertain, the effects of atmos- 



pheric refraction. We use t'le same instrument 

 with the same circle-division errors, and the tube will 

 be subjected to the same effects cf flexure when we 

 measure it in the two places. When we possess the 

 results of the measures extending from the north to 

 the south pole in a complete s\'stem, we shall be 

 certain that the\' will be independent of the 

 errors of the positions adopted for the stars 

 (ibserxed. The errors of observations in the zenith 

 will be minute : and it will be possible to correct 

 the observations of the circumpolar stars, bv means 

 of the new refraction, in such a manner that those 

 w ill be more accurate. Also, we shall have a system 

 of fundamental stars in all parts of the sk\- for adjust- 

 ing the various jjarts. These fundamental stars 

 will be observed in conjunction witli the zenith 

 and circumpolar stars. 



Basis of Right Ascensions. 



The elimination of the systematic errors in the 

 right ascensions is another problem. .^ fundamental 

 svstem should be based upon the position of the sun, 

 finalh' : but there is no necessity to observe the 

 transits of the sun in connection with all the 

 observations. It is possible to fix the positions of 

 the stars with that of the sun b}- means of the 

 oliservations which have been made, and the observa- 

 tions which mav be made, without adopting the 

 position of any star whose position is well deter- 

 mined. Observations of the declination of the sun, 

 combined with the observations of the stars, in anv 

 eiioch, will serve to determine the difference of right 

 ascension of these. 



We adopt a system of right ascensions as the 

 basis and with this proceed to the determination 

 of the systematic corrections in the various parts. 

 These corrections have a periodic character ; so that, 

 when thev occur opposite star groups, with a 

 difference of tweh'e hours in right ascension, the 

 sum of the corrections will be almost equal, with 

 contrary or opposite effect. From this periodic error 

 the results, when the correction of the clock is 

 determined by the observations of the stars in two 

 groups, at an interval of twelve hours, can be freed 

 of the periodic effect, if mit completeh-. at least in a 

 great measure. 



b"or the change or rate in the correction of the 

 clock, one uses the stars in the same group each day. 

 Between the stars of the same group there is little 

 variation, the positions will be \'ery exact and greatly 

 improved, but all those of a group can have the same 

 systematic error. 



For verif\'ing the true meridian-line one can 

 observe by day and by night an electric light, well 

 fixed in the meridian, as an artificial star at a 

 distance of one hundred meters to the north. The 

 position of this light has been determined by observa- 

 tions of circumpolar stars, and one will pursue 

 the determinations of this until the end of the work. 



For ascertaining the amount of flexure of the tube 

 of the instrument, one will make observations of the 

 stars by the two methods, by direct and reflected 



